In recent media coverage of studies reporting that coffee could be good for you, the Daily Telegraph reported that “Drinking a cup of coffee may add nine minutes per day to your life”, while ITV News used the images below.
ITV incorrectly attributed these numbers to the researchers themselves, as the relevant paper does not include any mention of either increase in life expectancy or minutes gained from a cup of coffee. So where do these numbers come from?
Well…., me. I provided the following quote to the Science Media Centre, who had sent me the papers under embargo.
“If these estimated reductions in all-cause mortality really are causal, then an extra cup of coffee every day would on average extend the life of a man by around 3 months, and a woman by around a month. Pro-rata, that’s as if that cup of coffee puts, on average, around 9 minutes on a man’s life, and around 3 minutes on a woman’s. So perhaps we should relax and enjoy it.”
I didn’t provide any explanation for these bold claims, and so am trying to rectify this now, and at the same time send my apologies to the researchers to whom the numbers were attributed.
Going from hazard ratios to changes in effective age and life-expectancy
Now another apology, and this time to any readers: it’s time for some statistical concepts. The standard output from these kind of studies is an estimate of the hazard ratio, which is the relative change in annual risk of death experienced by people exposed to whatever is being looked at. So, for example, the researchers estimated that the hazard ratio associated with an extra cup of coffee per day was 0.97 for men, which means that (keeping other lifestyle factors constant), the annual death rates of men were estimated to be 3% lower for each extra cup of coffee per day. The corresponding estimated hazard ratio for women was 0.99 per cup per day, which means that women drinking an extra cup of day had a 1% lower death rates. [Note these estimates assume all factors except coffee are held constant: in fact when they looked at the raw data they found people who drank the most coffee had the highest death rates, but that’s because they also tend to have other unhealthy habits]
These hazard ratios were not included in the press release, and are in any case a poor way to communicate impact: as we have pointed out before, describing risk in terms of its reduction or increase, rather than in absolute terms, can exaggerate the importance of any change.
Fortunately hazard ratios can be easily transformed to a measure of difference in ‘effective age’. As described in this (freely downloadable) paper How old are you, really? Communicating chronic risk through ‘effective age’ of your body and organs, each year a person ages is associated with a hazard ratio of 1.1, i.e. the annual risk of death increases by 10% for each year that people get older. This is remarkably constant across ages and populations.
Suppose a lifestyle factor is associated with a hazard ratio of h . Then (see Appendix for the gory details) exposure to the factor is equivalent to a change of t years of your effective age, where t is approximately 10 (h-1) for hazard ratios near 1.
If, as the researchers in this study estimate, a daily cup of coffee for a woman has a hazard ratio of h = 0.99, then this is equivalent to her effective age changing by 10 (0.99 - 1) = - 0.1 years, or essentially giving her the risk of someone around 1 month younger. Similarly, for men, a daily cup of coffee could be said to be associated with 3 months off their age.
So if the effect of coffee is causal and sustained throughout their life, this would mean an increase in life expectancy of 1 month for women and 3 months for men.
Going from life-expectancy to minutes per day
Assume an adult life is around 55–60 years. If a habit increases our life-expectancy by 1 year, that means our life has been increased by around 2%. That’s equivalent to around 30 minutes a day.
So an increase in life expectancy of 0.3 of a year associated with an extra cup of coffee in men is, pro-rata, around 9 minutes a day, and for women an increased life expectancy of 0.1 years is equivalent to around 3 minutes per cup.
Putting these two steps together, we get the rough approximation that a behaviour associated with a hazard ratio h throughout adult life is equivalent to a notional change of m = — 30 log h / log 1.1 minutes per day, or approximately 300 (1 — h) for hazard ratios near 1. An earlier version of this idea was described in my paper on Microlives.
Some examples are shown in the Table below
These values put the possible benefit of a daily cup of coffee into perspective, showing it is fairly minimal compared with the harms of other habits such as drinking, smoking, and sedentary behaviour, and the benefits and good diet and exercise.
These assessments are very rough and some are contested, particularly the positive benefit of the first alcoholic drink each day. And some are more ‘notional’ than others: statins are likely to have a substantial benefit for a small minority who would otherwise have a heart attack or stroke, and no benefit at all for the majority of consumers. So the ‘average’ benefit may not represent anyone. Nevertheless the notional half-hour encourages me to pop my daily Lipitor.
Both the investigators and the press release were admirably cautious in their conclusions and did not hype the story: while coffee may be slightly beneficial it is hardly a wonder drug. It’s a good example of how, if the story is genuinely interesting, exaggerations are unnecessary to get good coverage. And from the media response, it seems clear that these measures of ‘minutes a day’ are an attractive way of communicating impact of lifestyle.
But many arguments can be (and have been) raised against these notional minutes or hours of life lost or gained from a particular daily activity. These include:
The estimates of ‘minutes per day’ assume causality
They don’t: a cup of coffee can be described as associated with 9 minutes a day increase in life expectancy. I admit this is difficult to stick to, and causal language slips in easily and especially from media coverage. But this holds for any discussion of risk derived from observational studies - the confidence that the effects are causal depends on how well the statistical adjustment has been done, whether alternative explanations are feasible (residual confounding), the consistency of effects across many contexts, possible biological pathways and so on.
They are not ‘scientific’
I believe it is irresponsible to talk publicly about things increasing or decreasing risks without a giving a clear impression of magnitude. But the standard output from studies are relative risks for populations, such as hazard ratios, which are both difficult to comprehend and, as shown by multiple psychological studies, give an exaggerated impression of importance. The media audience are individuals and not scientists or policy makers. I believe we should use measures of absolute risk that are relevant to the individual, whether about statins, coffee or any of the other issues that litter the popular media.
People will take them too literally
I think (currently without empirical evidence) that people generally realise this is a notional and not a measurable figure, and that it is rather patronising to assume that they will be taken literally. But I agree that terms such as ‘notional’ should be attached, and I shall certainly try and do so from now on.
If each year older is associated with a hazard ratio of 1.1, then exposure to a risk factor with hazard ratio h is essentially equivalent to a change of t years in your effective age, where 1.1^t=h. Equivalently t = log h / log 1.1, where log is the natural logarithm. Using the approximation log (1+x) ≈ x for small x, then if h is near 1 then t ≈ 10 (h-1).